In the long, long history of professional baseball, across tens of thousands of games, there have been fewer than 300 no-hitters. Perfect games, in which no batter even reaches first base, are even rarer: fewer than two dozen in the past 100 years. And with the exception of one man, the Yankees’ Don Larsen, no one has ever thrown a no-hitter in a World Series game. Here, on the anniversary of that feat—a feat made all the more extraordinary in light of Larsen’s otherwise unspectacular career—LIFE.com remembers.

In baseball terms, the magnitude of Larsen’s no-hitter is hard to overstate. That it had never been done before in a World Series and has never been matched since is astonishing enough in a game where records fall and career-defining moments occur with dizzying frequency. But that Larsen hurled a perfect game against a team as jam-packed with talent and power as the ’56 Brooklyn Dodgers boggles the mind. Reese, Snider, Robinson, Campanella, Hodges, Furillo—these are names that baseball fans still utter with something close to reverence. And Don Larsen, of all people—not a superstar pitcher, but a workmanlike hurler—shut them down.

The fans, the press, his peers—everyone who knew and loved baseball (including Larsen himself) was dumbfounded.

“If Nolan Ryan had done it, if Sandy Koufax had done it, if Don Drysdale had done it, I would have nodded and said, ‘Well, it could happen,'” long-time Yankees public address announcer announcer Bob Sheppard (a.k.a., the Voice of God) once said. “But Don Larsen?”

The intensity of the competition between the Yankees and the Dodgers—and, for years, the “other” New York team, the Giants—makes many of today’s over-hyped sports rivalries feel tame. In the 1950s alone, the Yankees won six World Series (three against Brooklyn, one against the Giants); Brooklyn won one (against the Yankees); the Giants won one (in 1954—one of the few years that neither the Yanks nor the Dodgers made it to the Fall Classic). This, then, was the atmosphere in which Don Larsen took the mound on that fall day six decades ago. Game 5 of the 1956 Series was more than a baseball contest; it was another chapter in a long, storied struggle between two teams filled with some of the best players the game has ever seen.

Larsen, who pitched without a windup, needed only 97 pitches to retire 27 batters. In the bottom of the ninth, with the crowd of 64,519 going crazy, he threw Dodger pinch-hitter Dale Mitchell a high fastball. In fact, most of the players on the field at the time felt that it might have been too high. But home plate umpire Babe Pinelli, working the very last game of a remarkable 21-year career, called it a strike. Mitchell argued the point—but it was all over. Don Larsen had thrown the first, and still the only, no-hitter in World Series history. (The Yankees went on the take the Series, 4 games to 3.)

“Last night I was a bum,” LIFE reported Larsen murmuring incredulously in the hours after his perfect game, “and tonight everybody wants to meet me.”

After his brief, heady brush with fame subsided, Larsen’s career in the years following the ’56 Series was one of gradually dimming lights. He did win another Series ring with the Yankees in 1958 but, in true journeyman fashion, he would play for five more teams over the next 10 years. When he retired in 1967, his career won-loss record was a ho-hum 81-91—although his strong World Series record of 4-2 with an ERA of 2.75 suggests that the cool customer who chatted up his teammates in the dugout during his Game 5 perfect game truly relished the big stage.

“They can never break my record,” Larsen once said of his World Series perfect game. “The best they can do is tie it.” Almost 60 years later, baseball is still waiting for someone, anyone, to do just that. In the meantime, the sport and its fans are still celebrating Larsen’s improbable masterpiece.

George Silk—Time & Life Pictures/Getty Images

Don Larsen talks to the press at Yankee Stadium after his perfect game, Oct. 8, 1956.